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LINEAR PROGRAMMING & PRODUCT MIX

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USING THE DATA BELOW, PLEASE ASSIST WITH QUESTIONS 1 THRU 4:

YOUR COMPANY PRODUCES 2 PRODUCTS - MODEL A & MODEL B. THESE MODELS HAVE PROFITS OF $1000 & $2000 RESPECTIVELY. EACH MODEL IS PRODUCED IN A 3 STEP PROCESS. THE AMOUNT OF TIME USED BY EACH MODEL IN EACH PROCESS IS:
MODEL A MODEL B TOTAL TIME AVAILABLE
PROCESS 1 1 3 150
PROCESS 2 3 3 210
PROCESS 3 2 1 120

1) SKETCH THE SET THAT SHOWS THE COMBINATION OF MODEL A & MODEL B THAT CAN BE PRODUCED (FEASIBLE SET)

2) SKETCH OUT A FAMILY OF CONTOUR LINES THAT SHOW VARIOUS COMBINATIONS OF MODEL A AND MODEL B THAT WILL PRODUCE PROFIT OF $100,000 & $140,000

3) FIND THE COMBINATION OF MODEL A & MODEL B THAT MAXIMIZES THE FIRM'S PROFIT. WHAT IS THE FIRM'S PROFIT AT THIS PRODUCT MIX?

4) IF YOU COULD BUY EXTRA CAPACITY OF PROCESS 3, WHAT IS THE MOST THAT YOU WOULD BE WILLING TO PAY TO PURCHASE IT? PLEASE SHOW WORK & PROVIDE AN EXPLANATION.

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LINEAR PROGRAMMING & PRODUCT MIX guidance is offered.

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Let x1 and x2 be the units of Model A and Model B produced ...

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